Good question. I found the episode script and read the whole scene. It's clearly meant to be a joke - and Friends had a lot of corny jokes - but I don't get it. I haven't seen the episode, so maybe there's some crucial visual context missing. My best guess is that Chandler is referring to his "rule" about waiting to call women after a date, but I don't get the pigeon connection either.
– TypeIAMay 27 at 4:42

And it's funny because the process of how a bill becomes a law is not something the friends would usually talk about. It's a very mundane thing to choose to cover up a prior conversation, which is funny.
– only_proMay 28 at 16:36